Q24 / 60 · KVPY 2015 (SA) · Mathematics

Let $x, y, z$ be positive reals. Which of the following implies $x=y=z$ ?

  • A
    $x^{3}+y^{3}+z^{3}=3 x y z$
  • Correct answer
    B
    $x^{3}+y^{2} z+y z^{2}=3 x y z$
  • C
    $x^{3}+y^{2} z+z^{2} x=3 x y z$
  • D
    $\quad(x+y+z)^{3}=27 x y z$

Solution

For option (3) if $x=z=1$ and $y=2$ then option (3) is right. So by option (3) we can't say $x=y=z$. Remaining options implies $x=y=z$

Hence, the correct answer is option: 'B'.

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